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Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces

机译：用于扩展缺陷计算的莱迪思格林函数：远程力的计算和误差估计

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摘要

Computing the atomic geometry of lattice defects-e.g., point defects, dislocations, crack tips, surfaces, or boundaries-requires an accurate coupling of the local deformations to the long-range elastic field. Periodic or fixed boundary conditions used by classical potentials or density-functional theory may not accurately reproduce the correct bulk response to an isolated defect; this is especially true for dislocations. Flexible boundary conditions have been developed to produce the correct long-range strain field from a defect-effectively "embedding" a finite-sized defect with infinite bulk response, isolating it from either periodic images or free surfaces. Flexible boundary conditions require the calculation of the bulk response with the lattice Green function (LGF). While the LGF can be computed from the force-constant matrix, the force-constant matrix is only known to a maximum range. This paper illustrates how to accurately calculate the lattice Green function and estimate the error using a truncated force-constant matrix combined with knowledge of the long-range behavior of the lattice Green function. The effective range of deviation of the lattice Green function from the long-range elastic behavior provides an important length scale in multiscale quasicontinuum and flexible boundary-condition calculations, and measures the error introduced with periodic-boundary conditions.
机译：计算晶格缺陷的原子几何形状-例如点缺陷，位错，裂纹尖端，表面或边界-需要将局部变形与远程弹性场精确耦合。经典电位或密度泛函理论所使用的周期性或固定边界条件可能无法准确地再现对孤立缺陷的正确体积响应；对于脱臼尤其如此。已经开发出灵活的边界条件，以从缺陷有效地“嵌入”具有无限体积响应的有限尺寸缺陷中产生正确的远程应变场，从而将其与周期图像或自由表面隔离开来。灵活的边界条件要求使用晶格格林函数（LGF）计算体积响应。虽然可以从力常数矩阵中计算出LGF，但仅在最大范围内知道力常数矩阵。本文阐述了如何使用截短的力常数矩阵准确地计算晶格格林函数并估计误差，并结合了晶格格林函数的远程行为知识。晶格格林函数偏离远程弹性行为的有效范围为多尺度拟连续谱和灵活的边界条件计算提供了重要的长度尺度，并测量了周期性边界条件引入的误差。

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